Should "Intruding" be used here?
I don't quite know how to interpret the image, but here is a possibility:

Switch into edge or vertex selection mode. Press &#9096; CtrlR to add a loop cut through the face ring in question, making sure to slide the new loop all the way down to the loop below it.



Press S and then &#8679; ShiftZ to scale the new edge loop while locking the Z axis to get something like this: